1. Simple Effects And Factorial Design Hypotheses

2. Outline of Today’s Discussion 1.Simple Effects 2.Hypotheses for Factorial Designs

3. Part 1 Simple Effects

4. 1.Once we have found a significant interaction in a complex design, we must locate the source of the interaction using “simple effects”… 2.Simple Effect - The effect of one IV at one level of the second IV. 3.Sometimes these are called ‘simple main effects’. 4.Example: The simple effect of Factor A, at level B1.

5. Simple Effects Would someone please describe the dimensionality of this experiment? Example of Simple Effect From Shaughnessy, Zechmeister & Zechmeister http://en.wikipedia.org/wiki/Locus_of_control

6. Simple Effects Let’s see if we have an interaction… would someone please walk us through the “subtraction method” ? Example of Simple Effect From Shaughnessy, Zechmeister & Zechmeister

7. Simple Effects 1.In the sessions to come, we’ll have a more formal way of identifying an interaction (i.e., an ANOVA that tests the statistical significance of the interaction.) 2.For now, we’ll assume on the basis of the subtraction method that we have a significant interaction. Work with me here. :-) 3.In our 3 by 2 design, there are five simple effects…

8. Simple Effects There is a simple effect of Accident (factor A) at each level of Depression (factor B). So, that’s 3 of the 5 simple effects. When there is a significant interaction, look at simple effects. From Shaughnessy, Zechmeister & Zechmeister

9. Simple Effects Which of these simple effects do you suspect would be statistically significant, and why? When there is a significant interaction, look at simple effects. From Shaughnessy, Zechmeister & Zechmeister

10. Simple Effects There is also a simple effect of Depression (factor B) at each level of Accident (factor A). So, that’s 2 of the 5 simple effects. When there is a significant interaction, look at simple effects. From Shaughnessy, Zechmeister & Zechmeister

11. Simple Effects When there is a significant interaction, look at simple effects. Which of these simple effects do you suspect would be statistically significant, and why? From Shaughnessy, Zechmeister & Zechmeister

12. Simple Effects When there is a significant interaction, look at simple effects. Note: Since there are three depression levels at each accident type, we would need some post-hoc (Scheffe or Tukey or Dunnet) tests to determine which pairs differ from each other. From Shaughnessy, Zechmeister & Zechmeister

13. Simple Effects 1.Let’s consider “the big picture”… 2.That is, when you are beginning to analyze data from your complex design, it helps to have a plan for your analysis…

14. Simple Effects Decision Tree for Analyzing Complex Designs Post hoc tests e.g., Scheffe, Tukey, Dunnet, Bonferroni. Modified From Shaughnessy, Zechmeister & Zechmeister Post Hoc Tests Post Hoc Tests

15. Simple Effects 1.Potential Pop Quiz Question: What is the simplest possible complex design? 2.Potential Pop Quiz Question: In your own words, explain what is meant by the phrase “natural groups design”. 3.Potential Pop Quiz Question: In your own words, explain how researchers could use complex designs to test a theory of why natural groups differ.

16. Part 2 Hypotheses For Factorial Designs

17. In the population, the means will be the same across all levels of Factor A. In the population, the means will be the same across all levels of Factor B. In the population, differences among the levels of Factor A will be the same at each level of Factor B.

18. Hypotheses For Factorial Designs Consider a study in which a story is presented. The story contains either 0, 1, 2, or 3 violations of physical laws (e.g., gravity is suspended). Participants rate the plausibility of the story. The researcher investigates whether plausibility ratings depend on (A) the number of violations, and (B) the extent to which the participant is “manic”.

19. Hypotheses For Factorial Designs In the population, mean plausibility ratings will be equal across number-of-violations. In the population, mean plausibility ratings will be equal across “mania” levels. In the population, differences among the means for number-of-violations will be the same at each level of mania.

20. Hypotheses For Factorial Designs In the population, the interaction between Factor A and Factor B will be the same at each level of factor C. In the population, the interaction between number-of-violations and mania will be the same at each level of Gender. 3-Way Interaction

21. Analysis of Complex Designs What’s “wrong” with this graph? Shaughnessy,JJ, Shaughnessy, EB, and Zechmesiter, JS. Research Methods in Psychology, McGraw Hill.